#include <tgmath.h>
#include <gmp.h>
#include <mpfr.h>
#include <stdio.h>
#include <stdbool.h>

char *name = "Migdal et al, Equation (51)";

double f_if(float k, float n) {
        float r23112 = 1;
        float r23113 = k;
        float r23114 = sqrt(r23113);
        float r23115 = r23112 / r23114;
        float r23116 = 2;
        float r23117 = atan2(1.0, 0.0);
        float r23118 = r23116 * r23117;
        float r23119 = n;
        float r23120 = r23118 * r23119;
        float r23121 = r23112 - r23113;
        float r23122 = r23121 / r23116;
        float r23123 = pow(r23120, r23122);
        float r23124 = r23115 * r23123;
        return r23124;
}

double f_id(double k, double n) {
        double r23125 = 1;
        double r23126 = k;
        double r23127 = sqrt(r23126);
        double r23128 = r23125 / r23127;
        double r23129 = 2;
        double r23130 = atan2(1.0, 0.0);
        double r23131 = r23129 * r23130;
        double r23132 = n;
        double r23133 = r23131 * r23132;
        double r23134 = r23125 - r23126;
        double r23135 = r23134 / r23129;
        double r23136 = pow(r23133, r23135);
        double r23137 = r23128 * r23136;
        return r23137;
}


double f_of(float k, float n) {
        float r23138 = n;
        float r23139 = atan2(1.0, 0.0);
        float r23140 = 2;
        float r23141 = r23139 * r23140;
        float r23142 = r23138 * r23141;
        float r23143 = 1;
        float r23144 = r23143 / r23140;
        float r23145 = pow(r23142, r23144);
        float r23146 = k;
        float r23147 = r23146 / r23140;
        float r23148 = pow(r23142, r23147);
        float r23149 = r23145 / r23148;
        float r23150 = sqrt(r23146);
        float r23151 = r23149 / r23150;
        return r23151;
}

double f_od(double k, double n) {
        double r23152 = n;
        double r23153 = atan2(1.0, 0.0);
        double r23154 = 2;
        double r23155 = r23153 * r23154;
        double r23156 = r23152 * r23155;
        double r23157 = 1;
        double r23158 = r23157 / r23154;
        double r23159 = pow(r23156, r23158);
        double r23160 = k;
        double r23161 = r23160 / r23154;
        double r23162 = pow(r23156, r23161);
        double r23163 = r23159 / r23162;
        double r23164 = sqrt(r23160);
        double r23165 = r23163 / r23164;
        return r23165;
}

void mpfr_fmod2(mpfr_t r, mpfr_t n, mpfr_t d, mpfr_rnd_t rmd) {
        mpfr_fmod(r, n, d, rmd);
        if (mpfr_cmp_ui(r, 0) < 0) mpfr_add(r, r, d, rmd);
}


static mpfr_t r23166, r23167, r23168, r23169, r23170, r23171, r23172, r23173, r23174, r23175, r23176, r23177, r23178;

void setup_mpfr_f_im() {
        mpfr_set_default_prec(1424);
        mpfr_init_set_str(r23166, "1", 10, MPFR_RNDN);
        mpfr_init(r23167);
        mpfr_init(r23168);
        mpfr_init(r23169);
        mpfr_init_set_str(r23170, "2", 10, MPFR_RNDN);
        mpfr_init(r23171);
        mpfr_init(r23172);
        mpfr_init(r23173);
        mpfr_init(r23174);
        mpfr_init(r23175);
        mpfr_init(r23176);
        mpfr_init(r23177);
        mpfr_init(r23178);
}

double f_im(double k, double n) {
        ;
        mpfr_set_d(r23167, k, MPFR_RNDN);
        mpfr_sqrt(r23168, r23167, MPFR_RNDN);
        mpfr_div(r23169, r23166, r23168, MPFR_RNDN);
        ;
        mpfr_const_pi(r23171, MPFR_RNDN);
        mpfr_mul(r23172, r23170, r23171, MPFR_RNDN);
        mpfr_set_d(r23173, n, MPFR_RNDN);
        mpfr_mul(r23174, r23172, r23173, MPFR_RNDN);
        mpfr_sub(r23175, r23166, r23167, MPFR_RNDN);
        mpfr_div(r23176, r23175, r23170, MPFR_RNDN);
        mpfr_pow(r23177, r23174, r23176, MPFR_RNDN);
        mpfr_mul(r23178, r23169, r23177, MPFR_RNDN);
        return mpfr_get_d(r23178, MPFR_RNDN);
}

static mpfr_t r23179, r23180, r23181, r23182, r23183, r23184, r23185, r23186, r23187, r23188, r23189, r23190, r23191, r23192;

void setup_mpfr_f_fm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r23179);
        mpfr_init(r23180);
        mpfr_init_set_str(r23181, "2", 10, MPFR_RNDN);
        mpfr_init(r23182);
        mpfr_init(r23183);
        mpfr_init_set_str(r23184, "1", 10, MPFR_RNDN);
        mpfr_init(r23185);
        mpfr_init(r23186);
        mpfr_init(r23187);
        mpfr_init(r23188);
        mpfr_init(r23189);
        mpfr_init(r23190);
        mpfr_init(r23191);
        mpfr_init(r23192);
}

double f_fm(double k, double n) {
        mpfr_set_d(r23179, n, MPFR_RNDN);
        mpfr_const_pi(r23180, MPFR_RNDN);
        ;
        mpfr_mul(r23182, r23180, r23181, MPFR_RNDN);
        mpfr_mul(r23183, r23179, r23182, MPFR_RNDN);
        ;
        mpfr_div(r23185, r23184, r23181, MPFR_RNDN);
        mpfr_pow(r23186, r23183, r23185, MPFR_RNDN);
        mpfr_set_d(r23187, k, MPFR_RNDN);
        mpfr_div(r23188, r23187, r23181, MPFR_RNDN);
        mpfr_pow(r23189, r23183, r23188, MPFR_RNDN);
        mpfr_div(r23190, r23186, r23189, MPFR_RNDN);
        mpfr_sqrt(r23191, r23187, MPFR_RNDN);
        mpfr_div(r23192, r23190, r23191, MPFR_RNDN);
        return mpfr_get_d(r23192, MPFR_RNDN);
}

static mpfr_t r23193, r23194, r23195, r23196, r23197, r23198, r23199, r23200, r23201, r23202, r23203, r23204, r23205, r23206;

void setup_mpfr_f_dm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r23193);
        mpfr_init(r23194);
        mpfr_init_set_str(r23195, "2", 10, MPFR_RNDN);
        mpfr_init(r23196);
        mpfr_init(r23197);
        mpfr_init_set_str(r23198, "1", 10, MPFR_RNDN);
        mpfr_init(r23199);
        mpfr_init(r23200);
        mpfr_init(r23201);
        mpfr_init(r23202);
        mpfr_init(r23203);
        mpfr_init(r23204);
        mpfr_init(r23205);
        mpfr_init(r23206);
}

double f_dm(double k, double n) {
        mpfr_set_d(r23193, n, MPFR_RNDN);
        mpfr_const_pi(r23194, MPFR_RNDN);
        ;
        mpfr_mul(r23196, r23194, r23195, MPFR_RNDN);
        mpfr_mul(r23197, r23193, r23196, MPFR_RNDN);
        ;
        mpfr_div(r23199, r23198, r23195, MPFR_RNDN);
        mpfr_pow(r23200, r23197, r23199, MPFR_RNDN);
        mpfr_set_d(r23201, k, MPFR_RNDN);
        mpfr_div(r23202, r23201, r23195, MPFR_RNDN);
        mpfr_pow(r23203, r23197, r23202, MPFR_RNDN);
        mpfr_div(r23204, r23200, r23203, MPFR_RNDN);
        mpfr_sqrt(r23205, r23201, MPFR_RNDN);
        mpfr_div(r23206, r23204, r23205, MPFR_RNDN);
        return mpfr_get_d(r23206, MPFR_RNDN);
}